Centrosomes catalyse the formation of microtubules needed to assemble the mitotic spindle apparatus1. Centrosomes themselves duplicate once per cell cycle, in a process that is controlled by the serine/threonine protein kinase PLK4 (refs. 2,3). When PLK4 is chemically inhibited, cell division proceeds without centrosome duplication, generating centrosome-less cells that exhibit delayed, acentrosomal spindle assembly4. Whether PLK4 inhibitors can be leveraged as a treatment for cancer is not yet clear. Here we show that acentrosomal spindle assembly following PLK4 inhibition depends on levels of the centrosomal ubiquitin ligase TRIM37. Low TRIM37 levels accelerate acentrosomal spindle assembly and improve proliferation following PLK4 inhibition, whereas high TRIM37 levels inhibit acentrosomal spindle assembly, leading to mitotic failure and cessation of proliferation. The Chr17q region containing the TRIM37 gene is frequently amplified in neuroblastoma and in breast cancer5-8, rendering these cancer types highly sensitive to PLK4 inhibition. We find that inactivating TRIM37 improves acentrosomal mitosis because TRIM37 prevents PLK4 from self-assembling into centrosome-independent condensates that serve as ectopic microtubule-organizing centres. By contrast, elevated TRIM37 expression inhibits acentrosomal spindle assembly through a distinct mechanism that involves degradation of the centrosomal component CEP192. Thus, TRIM37 is an essential determinant of mitotic vulnerability to PLK4 inhibition. Linkage of TRIM37 to prevalent cancer-associated genomic changes-including 17q gain in neuroblastoma and 17q23 amplification in breast cancer-may offer an opportunity to use PLK4 inhibition to trigger selective mitotic failure and provide new avenues to treatments for these cancers.